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Your search keyword '"PEIRONE, ROBERTO"' showing total 4 results
Start Over Author "PEIRONE, ROBERTO" Topic dirichlet forms
4 results on '"PEIRONE, ROBERTO"'

2. Self-similar Energies on Fractals with Connected Interior

Author

Peirone, Roberto and Peirone, Roberto

Subjects
Eigenfunctions, Dirichlet forms, Fractals, Mathematics::Number Theory, [MATH.MATH-SP] Mathematics [math]/Spectral Theory [math.SP], [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]
Abstract

In this paper, I prove the existence of a regular eigenform for suitable weights, on fractals with the only assumptions that the boundary cells are separated and the union of the interior cells is connected. This result improves previous results, and works for many of the usually considered finitely ramified fractals.

Published
2009

3. Uniqueness of eigenforms on fractals - II.

Author

Peirone, Roberto

Subjects
*FRACTAL analysis, *GEOMETRIC analysis, *DIRICHLET forms, *MATHEMATICAL forms, *CHARACTERS sums (Mathematics)
Abstract

I give an explicitly verifiable necessary and sufficient condition for the uniqueness of the eigenform on finitely ramified fractals, once an eigenform is known. This improves the results of my previous paper [16], where I gave some necessary and some sufficient conditions, and with a relatively mild additional requirement on the known eigenform. The result of this paper can be interpreted as a uniqueness result for self-similar energies on finitely ramified fractals. [ABSTRACT FROM AUTHOR]

Published
2015
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4. Uniqueness of eigenforms on fractals.

Author

Peirone, Roberto

Subjects
*FRACTALS, *DIRICHLET forms, *EUCLIDEAN algorithm, *GASKETS, *EIGENFUNCTIONS, *INVARIANT subspaces
Abstract

I give some rather general criteria for the uniqueness of the eigenform on finitely ramified fractals. In particular, I characterize the uniqueness in the case of four vertices with some additional condition, and give some examples of non-tree symmetric fractals where the eigenform is not unique. [ABSTRACT FROM AUTHOR]

Published
2014
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